Friday, December 10, 2021

Answering Aristotle I.1 - The Basic Process

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Physics I.1 Although understanding something means we can reason from first principles, discovering these principles requires us to sort them out from the aggregate observations we are built to apprehend.

And do that over and over a hundred times per book. I only rarely go back to them. I thought what I'd do here is to extend this a little by discussing how Aristotle's insights hold up, how they compare to what I've been told they are, and so on.

There are two things that Physics I.1 brings to mind. The first is the actual evolution of physics, which in some places follow Aristotle's insight and in some placed doesn't. The other is that this discussion reflects the advice of Arnold Arons on the teaching of physics.

When I wrote about operational definitions (or will write about in the past), I used an example from Arnold Arons, most likely, that describes how the concept of temperature arose in physics. This is a relatively new idea, and we know exactly how it developed. And it definitely follows Aristotle's process. "The natural way" to proceed is to "start with that which is intelligible to us and then to move toward what is intelligible to the thing in itself." That is, we start with what we perceive about the world, and then we try to use that to determine the way the world actually works.

The first instance is temperature. This is a concept we all have a fairly intuitive understanding of, right? Well, not really. We have an understanding of "hot" and "cold," which was always a fairly ill-defined idea until Galileo. In order to construct a notion of temperature, we need to define a reliable way to compare "hot" and "cold," which is quite difficult. If you hold a book that has been sitting in a room for a long time, it feels neither hot nor cold, but if you touch marble, it feels cool. Finding a common understanding under such conditions is difficult. At the turn of the 17th century, Galileo invented his thermoscope, an instrument that held a glass bulb containing air and suspended in water that would rise and fall with changes in the state of the air (both the temperature and pressure state variables would cause these changes). It was only qualitative, but it was the first way in which our subjective idea of hot and cold could be related to the internal state of the things we called "hot" and "cold."

It would be another hundred years before Fahrenheit constructed reliable thermometers based on the relative thermal expansion of air to that of mercury or alcohol. This allowed a science of thermodynamics and a theory of engines to rise, but it did not tell us what temperature is. What was needed for that was the kinetic theory of gases, a statistical examination of the motion of air molecules. This would wait for another 200 years, after the atomic theory of matter was accepted and probability theory was on a sound footing. The temperature of the air became the average kinetic energy in the translational motion of its molecules. Which is not what your feeling, your apprehension, of hot and cold is about.

"Hot" and "cold" is about the rate of energy transfer from a material to you, which is why your book feels neutral and the marble feels hot. But, this too is explained by statistical mechanics. So, our basic ideas, the categories of our experience, led us to discover the idea of a measurable temperature, which in turn allowed us to discover what this meant to the air, and finally to even explain what our experience is really measuring.

This mirrors the point of Aristotle's Physics I.1 exactly.

I was going to offer a second example of the kind, the nineteenth's century's development of the idea of energy, which displaced the "imponderable fluids" of the 18th century (caloric, etc.). I think the story would further support Aristotle.

A counterexample, however, might be the late 20th century's search for fundamental particles. Here, the big minds theorized the existence of fundamental particles, but rather vaguely based on precise theories, and provided the material experimentalists, who then searched for them with amazingly powerful and expensive machines. At meetings, you would see maps of the parameter space, regions blocked off from where different experiments could measure. Experiments verified, experiments falsified, but experiments didn't drive the science. And neither did our perceptions. I cannot see how this follows Aristotle's program, although perhaps a longer view could make a good story of it.

It seems though, for most of its existence, physics followed something close enough to that program.

The other comparison that this brought to mind was an educational one. Maybe two, in fact. The first from Arnold Arons and the other from Edward Redish, although many of these insights I've seen elsewhere.

One of the more interesting admonishments of Arons' Teaching Introductory Physics is his insistence that concepts come before names [2]. This is part of his Socratic attempt to build students' physical intuition. The idea is to use identify the need for a concept, to start using the concept, before naming it. Even going to the point of admonishing students who use the term (e.g., "energy") before it is fully defined. Naming things gives people a feeling of understanding when they do not, and it relieves them enough that they ignore the rest of what's being said ("oh, that's energy -- let's get back to the important things, like "Hearthstone"). But you'll notice, this teaching style mirrors Aristotle's Physics I.1.

So it looks like Aristotle's approach to physics looks like the same approach physicists usually use both to investigate phenomena and to teach physics. This, at least, is a good sign for the rest of the book, despite its reputation.

[1] Most of this comes from Arnold Arons' Teaching Introductory Physics Part III: Introduction to the Classical Conservation Laws.

[2] This comes mostly from part I. I just skimmed Arons and couldn't find what I remembered. Is it Knight's Five Easy Lessons? Can't find it there, either. Probably Arons.

[3] He may also have said many of the same things in his Teaching Physics with the Physics Suite, which is also good (despite much very particular advice relating to the Physics Suite). The references for the articles are:

0. Redish, E.F., "Using Math in Physics: Overview." [arXiv]
1. Redish, E.F., "Using Math in Physics: 1. Dimensional Analysis." [arXiv]
2. Redish, E.F., "Using Math in Physics: 2. Estimation." [arXiv]
3. Redish, E.F., "Using Math in Physics: 3. Anchor Equations." [arXiv]
4. Redish, E.F., "Using Math in Physics: 4. Toy Models." [arXiv]
5. Redish, E.F., "Using Math in Physics: 5. Functional Dependence." [arXiv]
6. Redish, E.F., "Using Math in Physics: 6. Reading the Physics in a Graph." [Not Yet Published]
7. Redish, E.F., "Using Math in Physics: 7. Telling the Story." [Not Yet Published]

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